Are you wondering about how to do it through Amazon or how to produce mobi files?

Doing it through Amazon I don't know anything about - whether it can even be done or not.

To produce a .MOBI file though, you'll just need a converter. I personally use Calibre to make my mobi files. I save my document as an HTML file, import it into Calibre and export it into e-book format. It's not particularly complicated and there are guides online to help if you search for it.

If you have it published with Amazon (or uploaded to the site pending to be published), there is a previewer you can download that will provide a mobi copy of your book for your own review, you can then just send this to the reviewer. The previewer is there during the upload.

If you have it published through Smashwords, you can generate any file format of the book through your dashboard.

For published books, I always just buy the book myself and send it to them; with my math books especially, the bestseller lists are small enough that a single sale can swing the position considerably; every little bit helps! (not to mention you figure that you'll get 35-70% of the cost of the book back in your royalty at the end of the month).